11A - The unit circle
Degrees and radians:
Previously, you would have measured angles using degrees, where one revolution contains \(360°\). However, in VCE Mathematical Methods we will use radians to measure angles.
■ 1 radian is defined to be the angle made when an arc length of 1 unit is created on the unit circle. ■ As the circumference of the unit circle is \(2\pi\) units, there are \(2\pi ^c\) in 1 revolution. ■ Therefore, the relationship between degrees and radians is \(360^o=2\pi ^c\) |
GeoGebra: Visualising radians on the unit circle
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11A - Example 1: Converting between degrees and radians
Convert each of the following angle measurements into either degrees or radians.
(a) \(\frac{\pi}{6}^c\) (b) \(\frac{16\pi}{9}^c\) (c) \(45°\) (d) \(255°\) |
11A - Example 1: Video solution
11A - Example 1: Practice
Question 1: Convert each of the following angle measurements into either degrees or radians. (a) \(\frac{2\pi}{3}^c\) (b) \(\frac{7\pi}{5}^c\) (c) \(210°\) (d) \(350°\) 11A - Example 1: Solutions
Question 1: (a) \(\frac{2\pi}{3}^c=120°\) (b) \(\frac{7\pi}{5}^c=252°\) (c) \(210°=\frac{7\pi}{6}^c\) (d) \(350°=\frac{35\pi}{18}^c\) |